1/3 - (x+1)/5 = x/3 (only there are no parenthesis around the x+1 over 5... if that matters in this instance) ... and

(y+5)/12 = 3/4 - (y+1)/8 (once again, no parenthesis around the fractions with variables in these equations...)

My issue is figuring out whether if what I currently have is an acceptable answer or if there's actually a way to simplify it further... everything else i'm currently working on i feel pretty comfortable with. It just seems to be these two that frustrate me... any help is appreciated greatly:)

... oh, solve. but i just wanted to make sure my work was accurate. finding a common denominator and then, one friend suggested, getting rid of the denominator and solving the problem as 5 - 3x + 3 = 5x, and 2y + 10 = 18 - 3y +3.

You don't have to bother with getting common denominators. Just multiply through by whatever the common denominator would have been, had you converted.

By the way, you'll want to be careful with the grouping, so you don't drop signs. For instance, multiplying through the first equation by 15 will give you 5(1) - 3(x + 1) = 5(x), and this does not multiply out to what you've listed.